<p>We consider how we set out to formulate a parallel analytical molecular surface algorithm that has expected linear complexity with respect to the total number of atoms in a molecule. To achieve this goal, we avoided computing the complete 3D regular triangulation over the entire set of atoms, a process that takes time O(n log n), where n is the number of atoms in the molecule. We aim to compute and display these surfaces at interactive rates, by taking advantage of advances in computational geometry, making further algorithmic improvements and parallelizing the computations.</p>